This is your verification code, not one of your encryption keys.
You set this code on the verification code page, found under the profile page.
The purpose is to ensure that no-one is able to just reload a page when you walk away from a device.
you are being asked to verify yourself on every page because you indicated that you didn't want us to remember your username on this device, we take this to mean you are using a public device.
If you fail to enter the correct verification code, you will be logged off.